CAREER: Switching and Logic in Control

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0093762HespanhaIn this proposal we delineate a five year-research and education plan in the area of Automatic Control. The overall objective of this plan is to build the foundation for a career devoted to scientific research and its integration in the educational program at the University of Southern California.Our research and education efforts will be focused in the area of hybrid control systems, i.e., systems that combine continuous dynamics with discrete logic. We are particularly interested in supervisory control algorithms that utilize discrete logic for the purpose of online learning and adaptation. The use of logic in this context was proposed in the control literature more than fifteen years ago. Most of the early work was of a theoretical nature, motivated by the desire to construct universal controllers capable of stabilizing very large classes of systems. The universality of these controllers was achieved at the expense of very poor performance and the resulting algorithms could not be used in most practical applications. Since then a great deal of progress has been made in this area and now supervisory control is actually proposed as a technique to attain very high performance and robustness to sudden changes in the process or the control objectives.The scientific goal of our research is to develop a framework to expedite the analysis and design of learning algorithms that utilize switching and logic. Towards this end we will isolate the fundamental issues that arise in the design of supervisory control algorithms and explore them in a systematic fashion. We show in this proposal that although many of the algorithms proposed in the literature originate from fundamentally different approaches, they share key structures and exhibit several common properties. A common framework will provide a better understanding of their key features and limitations. We isolate here two specific topics that we judge crucial for the wide establishment of supervisory control:1. Extend the domain of application of these algorithms to the control of complex nonlinear systems. In particular, when only output-feedback is available and/or when there is significant measurement noise and unmodeled dynamics.2. Develop theoretical tools to optimize the performance of these systems. Here, performance should be understood both in a transient and in an asymptotic sense.